How do I Inspect and Correct my bone weight painting?
Inspecting and Repairing Vertex Weights


Toss Rubbish and Start Fresh.  Delete armature modifier.  Get well planned rest pose. Add armature modifier a second time and see if that eliminates problems.  Assuming you have not expended hours of paint time.  Otherwise read on.
Examine the glasses. Select Glasses.





View Solid. No Materials or Textures. 
Know that casual visual inspection of colors is not exact enough.  Slight color differences may be difficult to detect for the human viewer.  Clearly blender uses floating point numbers as the representation.
Know that some vertices are more difficult to see.  An exposed pinky is easier to see than an internal pink tongue.  Hair on Glasses makes the glasses difficult to see.
Local Mode. Numeric Keypad /. You should only see glasses.
Edit Mode
Press N to bring up the panel needed below.  





Disable [Limit Selection to Visible]  Make sure you can see through Model.  See Yellow arrow above.  Float mouse to see tooltip.
Enable View Weights
Select Nothing. Blender will indicate 0 vertices of XXXX selected.
Select the problematic vertex group related to bone in the Vertex group panel. UpperArm.Right. Click the select Button in the panel to select all vertices in the group.
Note and record how many vertices are selected.  This number will not be zero.  This is an error for the glasses.
More inspection. You can Grab g Translate and Move Vertices as extra verification. Shake mouse like you mean it.  Escape to reject the grab and keep vertices in original location.
Locate Vertex Weights Panel.  It will appear because some vertices are selected.  It will disappear otherwise. Make mental note to include in screen capture.
Take screen snapshot and update your images in your original question.  Make sure selection and vertex groups are showing. Your image should convey all bullet points above.
Make one of the selected vertices the active vertex with multiple Shift Click
Read how many groups in which this vertex has membership.  Your probably only want one for glasses, the head bone. Facial Areas require more care.
Delete all other groups but the head bone. Only the head bone group remains. This group deletion may be easier for the glasses since we can assume for simple purposes that no stretching should be seen.  Delete can be done in the vertex group panel or in the info panel in 3D View.  
Some of the inspection steps above are for education.





Next select the head and perform the same steps above. Use your judgement deleting groups. Skin is more pliable than plastic glasses.
Note in weight paint mode you can perform such tasks as making sure vertices have only the dominant one or two groups.  This can remove difficult mistakes and circumstances created by whomever.  
As always there are alternative ways to clean up the weights.  Direct Bone Parenting for example. Different question.
See basic and advanced tutorials. Ask a new question.